I think Mario Kart has the 3.2 update. I think there's a wiki page with the updat info around here somewhere. You can use brickblocker to remove the updates from iso's or you can install preloader and block updates that way. All your homebrew stuff should be fine, but if you have preloader already installed you'll have to reinstall it.

Once again, there is no game with 3.2. Mario Kart has 3.1, but contains the IOSes found in 3.2. (except IOS37) The only way to get the System Menu 3.2 WAD is to pack it yourself with NUS Downloader or rip it from bushing's semi-brick fix disc.

Updating to 3.2 will NOT touch the Homebrew Channel and the rest of your homebrew. One of the best ways is to use AnyRegion Changer.

Waninkoko's Firmware Upgrader 4.0 updates the System Menu, your channels, and certain IOSes. It will not touch any IOS you already have, such as IOS30. This preserves the fakesigning bug. Using this updater will not give you a custom IOS or System Menu.

It is highly recommended for you to use AnyRegion Changer to go to 3.2. Just make sure you don't scramble the regions up!